# Statistics Interview Questions

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**Why do we have n -1 in the denominator in the variance formula, instead of n**

If we use the intuitive denominator of n in the variance formula, we will underestimate the true value of the variance and the standard deviation in the population.

This is referred to as a biased estimate.

However, if you divide by n -1 instead of n, the variance becomes an unbiased estimate hence we use n -1 in the degree of freedom formula

**2. What is Expected Value?**The expected value is really a form of weighted mean: it adds the ideas of future expectations and probability weights, often based on subjective judgment.

For example, let's assume a new subscription service is testing its new pricing model

A: 15$ / month & B:20$ / month

The marketer from webinars gets leads after interview and records the responses

5% of the attendees prefer plan A & 15% prefer plan B, rest 80% don't agree with both.

so the Expected value is 0.05*15+0.15*20+0.0*80 = 18

3. What is a Permutation test?

Permute means to change the order of a set of values.

The first step in a permutation test of a hypothesis is to combine the results from groups A and B (and, if used, C, D,…).

Null hypothesis — the treatments to which the groups were exposed do not differ.

We then test that hypothesis by randomly drawing groups from this combined set and seeing how much they differ from one another.

Steps:

1: Combine the results from different groups into a single data set.

2: Shuffle the combined data & then randomly draw (without replacement) a resample of the same size as group A (clearly it will contain some data from other group)

3: From the remaining data randomly draw (without replacement) a resample of same size as group B

4: Do the same for group C,D,….

5: Whatever statistic or estimate was calculated for the original sample (Eg: difference in group proportions) calculate it for resamples, & record this constitutes one permutation iteration

6: Repeat all steps r times to yield permutation distribution of test statistic

Now go back to the observed difference between groups and compare it to the set of permuted differences. If the observed difference lies well within the set of permuted differences, then we have not proven anything — the observed difference is within the range of what chance might produce. However, if the observed difference lies outside most of the permutation distribution, then we conclude that chance is not responsible.